Intermediate Statistical Modeling in R

Effect sizes were introduced in Part 1 of this course series as a way to quantify how each explanatory variable is connected to the response. In this chapter, you'll meet some high-level tools that make it easier to calculate and visualize effect sizes. You'll see how to extend the notion of effect size to models with a categorical response variable. And you'll start to use interactions in constructing models to reflect the way that one explanatory variable can influence the effect size of another explanatory variable on the response.

In many circumstances, an effect size tells you exactly what you need to know: how much the model output will change when one, and only one, explanatory variable changes. This is called partial change. In other situations, you will want to look at total change, which combines the effects of two or more explanatory variables. You'll also see an additional, but limited way of quantifying the extent to which the explanatory variables influence the response: R-squared. Finally, we'll describe the notion of degrees of freedom, a way of describing the complexity of a model.

This chapter examines the precision with which a model can estimate an effect size. The lack of precision comes from sampling variability, which can be quantified using resampling and bootstrapping. You'll also see some ways to improve precision using mathematical transformations of variables.

In this final chapter, you'll learn about why you'd want to avoid collinearity, a common phenomenon in statistical modeling. You'll wrap up the course by discussing some of the ways models can be improved by involving the modeler in the design of the data collecting process.